Let A = {n $$\in$$ N : H.C.F. (n, 45) = 1} and

Let B = {2k : k $$\in$$ {1, 2, ......., 100}}. Then the sum of all the elements of A $$\cap$$ B is ____________.

The value of the integral

$${{48} \over {{\pi ^4}}}\int\limits_0^\pi {\left( {{{3\pi {x^2}} \over 2} - {x^3}} \right){{\sin x} \over {1 + {{\cos }^2}x}}dx} $$ is equal to __________.

Let $$A = \sum\limits_{i = 1}^{10} {\sum\limits_{j = 1}^{10} {\min \,\{ i,j\} } } $$ and $$B = \sum\limits_{i = 1}^{10} {\sum\limits_{j = 1}^{10} {\max \,\{ i,j\} } } $$. Then A + B is equal to _____________.

Let $$S = (0,2\pi ) - \left\{ {{\pi \over 2},{{3\pi } \over 4},{{3\pi } \over 2},{{7\pi } \over 4}} \right\}$$. Let $$y = y(x)$$, x $$\in$$ S, be the solution curve of the differential equation $${{dy} \over {dx}} = {1 \over {1 + \sin 2x}},\,y\left( {{\pi \over 4}} \right) = {1 \over 2}$$. If the sum of abscissas of all the points of intersection of the curve y = y(x) with the curve $$y = \sqrt 2 \sin x$$ is $${{k\pi } \over {12}}$$, then k is equal to _____________.